1. An article in Technometrics ["Validation of Regression Models: Methods and Examples" (1977, Vol. 19(4), p. 425)] presented the following data (which have been rounded to the nearest whole value) on the motor fuel octane ratings of several blends of gasoline: 89 99 90 92 93 88 88 91 95 88 90 83 88 93 88 90 84 90 92 91 93 94 88 92 90 91 91 88 94 97 89 90 39 91 89 89 90 84 92 92 90 92 88 93 91 93 89 92 88 94 87 87 89 90 90 91 85 91 94 89 93 90 87 90 91 91 93 93 92 93 89 100 90 87 90 96 91 88 92 a. (5 points) Construct a frequency distribution for these data by filling in the table below. Use 8 bins. Lower limit Upper limit Midpoint Frequency Relative frequency b. (5 points) Use the frequency distribution on the previous page to construct a histogram for these data.An article in Transactions of the institution of Chemical Engineers (1956, Vol. 34, pp. 280293) reported data from an experiment investigating the effect of several process variables on the vapor phase oxidation of naphthalene. A sample of the percentage mole conversion of naphthalene to maleic anhydride follows: 4.2, 4.7, 4.7, 5.0, 3.8, 3.6, 3.0, 5.1, 3.1, 3.8, 4.8, 4.0, 5.2, 4.3, 2.8, 2.0, 2.8, 3.3, 4.8, 5.0. a. (5 points) Calculate the sample mean, sample variance, and sample standard deviation. Feel free to use your calculator. b. (5 points) Construct a box plot of the data,_and mark the location of outliers (if any} with an asterisk. 3. (5 points] Using your calculator, construct a normal probability plot for the octane data from problem 1, and make a sketch of that plot below. From the plot you sketched, does it seem reasonable to assume that octane rating is normally distributed